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Find the sum to 'n' terms if n^(th) term...

Find the sum to 'n' terms if `n^(th)` term is given by `n^(2)+2^(n)`

Text Solution

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`T_(n)=n^(2)+2^(n)`
`thereforeS_(n)=sumT_(n)=sum(n^(2)+2^(n))=sumn^(2)+sum2^(n)`
`=(n(n+1)(2n+1))/(6)+(2^(1)+2^(2)+2^(3)+......+2^(n))`
`=(n(n+1)(2n+1))/(6)+(2(2^(n)-1))/(2-1)`
`=(n(n+1)(2n+1))/(6)+2(2^(n)-1)`
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